Dominance

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This is used in many contexts, but the general meaning is that something is uniformly better than something else. For example, consider two activities in a linear program, say LaTeX: j and LaTeX: k, such that:

  • LaTeX: j has greater cost: LaTeX: c_j \ge c_k
  • LaTeX: j produces less of each requirement: LaTeX: A_{i, j} \le A_{i, k} for LaTeX: i such that we require LaTeX: A_{i,*}x \ge b_i
  • LaTeX: j consumes more of each resource: LaTeX: A_{i, j} \ge A_{i, k} for LaTeX: i such that we require LaTeX: A_{i,*}x \le b_i
  • LaTeX: j produces or consumes at the same rate of goods to be conserved: LaTeX: A_{i, j} = A_{i, k} for LaTeX: i such that we require LaTeX: A_{i,*}x = b_i

Then, activity LaTeX: k dominates  activity LaTeX: j.


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